Electrical ballistic computing system



May 5, 3.953

ELECTRICAL Filed May 5l 1951 2 Sheets-Sheet 1 .'3 .L 33 l ris l? TVQ i5 SOURC SGURCE OUTPUT L x Va SOURCE x6 a CQ :\.w I. E ci\ 8Go N \`J 7Go N U c@ -9\\ D i \CALCULAT: DATA.

EXPERMENTAL MTAA (M Tama oF FMGHT m SECONDS i I E 2 INVENTOR.

WILUAM R. WELTY.

May 5, ES w. R. WEL-IY 133833,47@

ELECTRICAL BALLISTIC COMPUTING SYSTEM Filed May 51, 1951 2 Sheets-Sheet 2 2? Fsnscx AMPLIFIER I-2' +V@ If,

SOURCE SOURCE 32V n-IFfEIEII Svo 16 MIXER IIIEaIIIIIIIsII :E i E s I i: l 57 I 5 I i l i l l [5S P 42j -cIJMPuTIIIIIf;"- O l 1 I S SYSTEM O R' g +V@ I I4 I I@ '5T-w a I 351 I DIFFRsIcE 'simo MIXER MELHANISM l E INVENTOR. WILLIAM R. WELTY. BY

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iinited ftates iatent ELECTRL'CL BALLSTIC COMPUTING SYSTEM Wiliiam R. Welty, West Los Angeies, Calif., assigner, by mesne assignments, to Hughes Aircraft Company, a corporation of Deiaware Application May 3i, 1951, Serial No. 229,091

:.0 Ciaims. (Ci. 23S-61.5)

The present invention relates to an electrical computing system and more particularly to an electrical computing system for computing the value of an unknown as a function of a plurality of variables, one of which is dependent upon two others of the plurality of variables.

More specifically, although the basic concept of the invention is applicable to any electrical computing system of the type described above, it is readily adaptable to velocity computing systems for relatively moving objects, and is particularly suitable to ballistics computing systems for computing the average velocity of a projectile relative to the object from which the projectile is discharged or fired. Still further, the invention will be described with particular reference to ballistics computers for airborne objects, it being understood, of course, that the principles disclosed herein are applicable to ballistics computers for objects traveling through media other than lill'.

ln aircraft ballistics computers, one of the essential variables that must be determined accurately is the average velocity of the projectile relative to the aircraft as a function of time of iiight of the projectile from the air craft to the target. With this variable accurately determined. the computer may compute the product of the time of tlight and the average relative velocity of the projectile and present a tiring signal which will insure a target hit.

in theory. the variable average relative velocity of the projectile is a function of air density, air speed of the aircraft, initial velocity of the projectile relative to the aircraft, time of iiight of the projectile, and gravity. Since the time of liight ofthe projectile is relatively short, gravity may be neglected without any appreciable effect on the accuracy of the desired result. Accordingly, the average velocity can be determined with the precision required for ballistics computers only by proper evaluation of the remaining variables. ln considering air density, it is apparent that this is a function of both pressure and temperature, in accordance with the well-known gas law. as set forth below.

Several prior art devices have been devised to compute the average velocity variable, but each of these has proved to be ineffective both in theory and in practice. in one prior art arrangement, the air density is assumed to be proportional to air pressure, no weight being giveneither to air speed of the aircraft. or to temperature in determining the average relative velocity. In another prior art arrangement. the average velocity is assumed to be a straight line function of the initial velocity minus an air density factor, no consideration being given to the air speed of the aircraft. From the theory outlined above. it is apparent that neither of these prior art systems will produce a sufficiently accurate result for a ballistics computer. ln practice, these systems have been proved to be highly inaccurate when compared with known experimental data.

The present invention discloses a novel approach to the design of a ballistics computer which overcomes the 2,333,1i Patented May 5, i958 ice disadvantages of the prior art systems and produces a result which is, substantially identical with that indicated by experimental data. According to this invention, consideration is first given to the available experimental data on the average projectile velocities at various relative air densities for zero air speed of the aircraft. A circuit is designed which matches this experimental data with a high degree of accuracy. The circuit is then modified to incorporate aircraft velocities as a variable, The resulting circuit is then analyzed theoretically to evaluate properly the various circuit constants. Finally, the theoretical circuit is mechanized into a computer which evaluates all ol the variables and produces a resultant indication for the average velocity of the projectile which fully satises the available experimental data.

The complete mechanization of the computer includes a first computing circuit for computing the unknown average velocity as a function of all of the variables in accordance with the theoretical equations. This computing vcircuit includes a variable circuit element representing a factor which is a function of the air density. A second computing circuit computes this factor as a function of the variables air density, initial velocity of the projectile and air speed ot' the aircraft. The computation of the factor by the second circuit is then utilized by any suitable means to adjust the value of the variable circuit element in the lirst computing circuit.

it is again emphasized, however, that the computing system of the present invention is applicable to fields other than ballstics computers. Thus, the principle of the invention may be applied to an electrical computing system for computing the value of an unknown X as a function of a plurality of variables, v, w, x, y, one of the plurality of variables v being a function of x, y and a variable z. The lirst computing circuit would compute X, while the second computing circuit computed x. The solution obtained by the second circuit would be applied to the first circuit.

Accordingly, it is an object of the present invention to provide an electrical computing system :for computing the value ot` an unknown as a function of a plurality of variables, one of which is dependent upon two others of the plurality of variables.

An additional object of this invention is to provide a system for accurately computing the average relative velocity between a pair of objects moving at varying velocities relative to each other.

Another object is to provide a system for computing the average velocity of a projectile relative to the object from which the projectile is discharged as a function of the time of flight ofthe projectile.

A further object is to provide a ballistics computer which evaluates all of the essential variables involved in computing the average velocity of a projectile to produce a result which fully complies with experimental ballistics curves.

Still another object is to provide a ballistics computer which indicates the average velocity of a projectile in terms ot' air speed of the aircraft. initial velocity of the projectile, air density, and time of flight of the projectile.

The novel features which are believed to be characteristic of the invention, both as to its organization and method of operation, together with further objects and advantages thereof, will be better understood from the following description considered in connection with the accompanying drawings in which several embodiments of the invention are illustrated by way of examples. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only, and are not intended as a definition of the limits of the invention.

Fig. 1 is a circuit diagram of a network for computing the average relativcwelocity of a projectile at zero all* speed of the aircraft;

Fig. 2 is a graph of experimental data and curves calculated from the network of Fig. 1;

Fig. 3 is a circuit diagram of a modication of the network of Fig. l, which incorporates variable air speed of the aircraft;

Fig. 4 is a schematic diagram of one form of ballistics computer according to the present invention; and

Fig. 5 is a schematic diagram of another form of ballistics computer.

Referring now to Fig. l, there is shown a circuit diagram of a network which has been found empirical to match thc known ballistics curves for zero air speed of the aircraft tiring the projectile. This network comprises a pair or' serially connected variable resistors 11 and 12 connected as a voltage divider across a source t3 of V0 input signals, where V0 is the muzzle velocity of the projectile, that is the initial velocity ot the projectile rela.- tivc to the aircraft at the instant of firing of the projectile. For any given projectile and tiring mechanism. VQ is a constant and may readily be converted into an electrical signal t'or appiication to the network or Fig. l,

Resistor 1l constitutes one variable o`t` the networit, and its .setting represents the time or tlight z or the projectile from the aircraft to the target. Resistor l2 constitutes the other variable of the network, and its setting represents the t'actor i', denecl more particularly below, which is an inverse function of the air density p. Terminals l5' and 1G are the output terminals of the network, and the signal appearing thereacross. as demonstrated below, constitutes the output signal Vm. where Vm is the average velocity of the proiectile relative to the aircratt during the time of llight t. Preferably, terminals G, and one terminal E4 or source i3, are returned to ground to complete the network.

In operation. the constant V0 will have been determined previously and set into the network. The factor r will be measured during the tiight of the aircraft. or prior to tiring if the aircraft is stationary, and, by mechanism described hereinafter` will determine the setting of resistor il for any given tiring operation. With this setting of V0 and r. resistor il will be varied at a predetermined rate in accordance with the variation in the time of flight t. In practice, resistor il will be varied automatically by a mechanism, shown in Fig. 4 responsive to time of flight t as soon as t decreases to a predetermined value. This synchronous variation of resistor ,t1 is indicated schematically by dashed line 17 in Fig. l.

A comparison of the calculated responsive curves for the network or Fig. l and experimental data for a given projectile is shown in Fig. 2. The experimental data was obtained by measuring the range of the projectile for various times of flight, with relative air density p/p as the parameter, where p0 is a constant equal to the density of one atmosphere at a standard temperature. The average relative velocity Vm was computed as the ratio of the range to the time ot` flight.

From `Eig. 2, it can be observed that the calculated curves for the network of Fig. l match extremely well the experimental data obtained. The divergence between the calculated and experimental results or any given air density parameter is of such small magnitude as to be negligible for all practical purposes.

As pointed out above. it now ecomes necessary to consider the variable Vn, thc air speed ot the aircraft, in order to adapt the computer for universal application. The logical attempt is to return the t'ree end of resistor l2 to Vm since. as t approaches innitv, Vm approaches -Vy Stated differently, it` it is assumed that the projectile never hits thc target or ground= the projectile decelerates with time ot flight and finally stops as t approaches infinity. at which time Vm approaches Vm rlie modilied network is shown in F 3, where a source 1S of Va input signals has one terminal i9 connected to the free 4 end of resistor 12, the other terminal of source 18 being connected to ground, or terminal 16.

The equation for the network of Fig. 3 is:

By definition, the general equation of motion for Vm, in terms of the instantaneous velocity v of the projectile.

Combining Equations l, 2, and 4, to obtain v as a function of Va, V0, t, and r, results in:

Combining Equations l, 3. and 5 results in:

Cit

To eliminate t from Eguation 7, (r-t-f) may be replaced by a function of v from Equation 6, and

In order to convert Equation 8 into the well-known ballistics equation wherein v is dependent on only v and p, and remembering that r has been defined as an inverse function of p, the equation for r, in terms of p, is:

where K is a constant, or

essere Since the function,(T/'Wl-/P/2 is relatively diicult to mechanize, an approximation of this function, from the first two terms of the binomial expansion, yields:

Wanneer/Ovale Vfl/21a or s Vae-V (wwwa-W 10) Now, it can be shown that for all values of VOZ'JZVM which is the range of interest, the error introduced into the result by the approximation has a maximum value of 2 percent.

Accordingly, the use of Equation l is justified. Therefore, rewriting Equation 9, in terms of Equation where C is a constant determined empirically from the network of Fig. l.

Accordingly, evaluating Equation l1 for V=O, and comparing this with Equation l2, results in:

KV0i/2=C Substituting Equation 13m Equation ll presents:

CVO (14) Finally, using the ideal gas law P=pRT, where P and T are absolute pressure and temperature, respectively, and R is the known gas constant, Equation 14 can be rewritten as:

CVQRT TPt Vari/.i 19) where D-CVOR, all known or evaluated constants.

It is apparent that Equation 16 can be mechanized by any system which compares the magnitude, of the factor rP(l/0}-1/z Vfi) to the magnitude of the factor DT, and adjusts the value of r until equilibrium. One embodirnent ot` an electrical system for performing this function, and its connections to the network of Fi. 3, is illustrated in Fig. 4.

Referringy now to Fig. 4, a pair of positive input voltages proportional to V0 and Va, respectively, are applied to the input terminals of a linear mixing circuit 2 for producing an output signal whose magnitude is proportional to P(V0l/2V). One suitable form of circuit 2 for accomplishing this result, as shown in Fig. 4, is an impedance network comprising a pair of series connected resistors 22 and 23 having their common junction connected to ground through a potentiometer, generally designated 211.. The tree ends of resistors 22 and 23, which constitute the input terminals of mixing circuit 21, are coupled to the sources, respectively, of -l-Vo and -l-Va potential. Potentiometer 24 has the position of its movable tap 25 determined by the pressure variable P. Any conventional means, such as a static pressure line coupled within the limits ot accuracy of the computing system.

It is understood, of course, that circuit 21 may be of any well-known form, other than that illustrated in Fig. 4. Thus, impedances other than resistors may be utilized, or conventional amplifiers may be substituted for resistors 22 and 23. Similarly, potentiometer 24 may be replaced by other forms of im pedances, or by any well-known cornmon load device. Accordingly, it should be apparent that circuit 21 is merely illustrative, and that any linear mixer for producing an output signal proportional to the sum ot' linear functions of the input signals. in the ratio set forth above, is contemplated for circuit 21.

The output potential of circuit 21 is applied across a variable circuit element, such as an r potentiometer 26 through an isolation stage 27 in order to limit the loading of one of potentiometers 24 and 26 by the other. @ther suitable forms of the variable circuit element are a vari able gain amplier or a variable transformer. Isolation stage 27 may take any suitable form, the particular form illustrated in Fig. 4 comprising a high impedance, such as a resistor 28, connected in series with a feedback amplitier 2). One suitable form of amplifier 29 is a cathode follower.

Potentiometer 26 has the setting of its movable tap 31 determined by the mechanism described below so that the potential between tap 31 and ground is equal to rP(V0-l/2Va). This potential is applied to one input terminal of a mixer 32 through a coupling impedance, such as a resistor 33. Mixer 32 has its other input terminal connected to the output terminal of an amplifier 34 through a coupling impedance, such as a resistor 3S. Ampliiier 34 is utilized to produce an output signal proportional to the temperature parameter T, that is a signal equal to DT, where D is a constant, as set forth in connection with Equation i6. Accordingly, a source 39 applies a potential equivalent to temperature T to amplitier 34 which has an amplification ratio of D. Amplifier 34 may be any suitable vacuum tube ampliiier. or a suitable step-up transformer.

Mixer 32 is any conventional difference amplilier for producing an output signal that is linearly related to the difference of linear functions of the input signals. Suitable forms of mixer 32 are illustrated in Fig. 2.45 at page 119 of Electronics Experimental Techniques by William C. Elmore and Matthew Sands, published in 1949 by McGraw- -lill Book Company, lnc., and which is hereby incorporated by reference in this application.

ri`he output of mixer 32 is lapplied to the input terminals ot' a conventional servo mechanism 36 which controls the position ot` tap 3i ot` potentiometer 26 and of resistor l2 by a conventional mechanical linkage, generally designated 37. Servo mechanism 36 operates in a conventional and well-known follow-up manner to adjust the value of thc resistance of potentiometer 31. to bring the input signal applied to mechanism 36 to its zero or null value.

In operation. V0 is predetermined for each projectile and tiring mechanism and is set in as a tixed signal applied to one input terminal of circuit 21, either from source 13 or from an independent source. V,1 is the air speed ot the aircraft, and may be determined in any convenient and conventional manner. One means for obtaining V., is a Mach meter with a transducer for converting the meter indication into an electrical signal. Va is converted into an electrical signal, either in source 18 or in an independent source, which is applied to the other input terminal of circuit 2l. The temperature T is determined in any conventional manner, such as a temperature probe, converted into an electrical signal in source 39. and applied to the input terminals of amplier 34.

Vith this setting ot the system of Fig. 4, servo mech :in Lm 36 operates automatically to vary the value of potentiometer 26 until DT is equal to rPlVg-'VVzI/a), as set forth in Equation 16. Resistor 12 is varied by mechanism 56. simultaneously with the variation of potentiometer 26. so that the value of r represented by resistor l?. corresponds to the value olr represented by potentiometer 26.

The remaining variable is the time of flight t, represented by the value of variable resistor 11. ln practice, resistor 1l is continuously varied by a computing system. generally designated 33. through linkage 17. Computing system 38 solves for time r the general equation:

where R is the range between the aircraft and the target, and R is the rate or change of range R.

Since computing system 33 forms no part of the present invention. system 38 is not shown in detail in this application. However. it is clear that system 38 may be any servo system tor solving Equation i7 by varying i until the two -sides or' Equation 17 are equal. it is thus seen that the computing system ol Fig. -l operates simultaneously with computing system 38 to solve for variables Vm and t.

in some instances. computing system 33 may present the r Function in terms ol l/lrather than as a direct proportionality. Accordingly, the system ot` Fig. 4 may be modified to operate with the l/'r variable. One such arrangement is illustrated in Fig. 5.

Referring now to Fig 5, D amplifier 34 has its output terminals coupled across a potentiometer 56 which functions as a l/'l' potentiometer having its center tap Si connected io one input terminal of mixer 32 through resistor 53. Mixer 32 has its other input terminal coupled to the output terminal of circuit 2l through a resistor 55 pair of series connected variable resistors l and 4.a. are coupicd between terminal 'X9 of the wVn source and the positive terminal of the Vn source. terminal 14 of the -i-Vn source being connected to grounded output terminal 16. A l/r computing system S3 has one pair of its input terminals connected to terminals i5 and 16, the Vm output terminals. and controls the variation of resistor y-ll through a linkage i7'. System 53 may be a servo system. similar to system 3S. for varying l/'t until Vm is equal 'to In operation. mixer 32 equates the quantity to the quantity P(Vn+1/2Va) to actuate mechanism 36 which simultaneously varies the position of trip 5l of l/r potentiometer 56 and the magnitude or l/r resistor 2. through linkage 37. System varies l/r resistor di in the same manner as system 33 of Fig. 4 varies t resistor 1l. lt can readily be seen that the equation for Vm in the circuitof Fig. Sis:

l, l j V Vm iiiU 1' 4 tibi iHH/r init/f l, "Tijn-"lira l-----PE t (in) lt is thus seen that the present invention discloses a Dallistics computing system which considers all of the variables essential to a proper determination of the average relative velocity between the aircraft and the projectile. In this manner, the result attained has a degree of accuracy, far greater than that obtained by the prior art devices. The over-all result of this invention is the production of a ballistics computer which, for the i'irst time, has the degree of accuracy required to render the computer an asset to an aircraft computing system.

What is claimed as new is:

l. A ballistics computer for computing the average velocity Vm ot a projectile discharged from an aircraft relative to the velocity Vg of the aircraft. said computer comprising: a rst circuit tor producing a lirst electrical signal proportional to Pi'Vu-l-/z Vg), where P is the air pressure and V0 the initial velocity ot` the projectile; a iirst variable circuit element electrically coupled to said first circuit for producing7 a second electrical signal proportional to said irst electrical signal multiplied by a factor r; a second circuit for producing a third electrical signal proportional to DT, where D is a predetermined constant and T is the air temperature; a mixer for combining said second and third signals to produce an output signal proportional to the difference between said second and third signals; a computing circuit for electrically solving the equation:

rVn--tVn where l is the time of flight of the projectile from the aircraft to the target, said computing circuit including a second variable circuit element representing the factor r; and follow-up means coupled to said first circuit element and responsive to the output signal of said mixer for varying said first circtiit element to reduce the output signal of said mixer to zero, said follow-up means being coupled to said second circuit clement for varying said second circuit element simultaneously with the variation of said first circuit element.

2. A ballistics computer for computing the average velocity Vm or a projectile discharged from an aircraft relative to the velocity Vn of the aircraft. said computer comprising: a lirst circuit for producing a first electrical signal proportional to P(V0+1/2V) where P is the air pressure and Vo is the initial velocity of the projectile; a second circuit for producing a second electrical signal proportional to DT, where D is a predetermined constant, and T is the air temperature; a rst 'variable circuit element electrically coupled to one of said circuits for producing a third electrical signal proportional to the signal produced by said one circuit multiplied by a linear t`unction ot` a factor r; a mixer for combining said third signal and the signal produced by the other of said circuits to produce an output signal proportional to the dilerence between the combined signals; a computing circuit for electrically solving the equation:

'fr ri-t where t is the time ot' ight of the projectile from the aircraft to the target, said computing circuit including a second variable circuit element representing a function ot the lactor r similar to said linear function; and follow-up means coupled to said tirst circuit element and responsive to the output signal of said mixer for varying said lirst circuit element to reduce the output signal of said mixer to zero, said follow-up means being coupled to said second circuit element for varying said second circuit element simultaneously with said tirst circuit element.

3. A ballistics computer for computing the average velocity Vm ol:l a projectile discharged from an aircraft relative to the velocity V,1 of the aircraft. said computer comprising: a first computing circuit for electrically solving for r a trst equation DT-1'P(VO}-1/z Va=0, where D is a predetermined constant. '1` is the air temperature, P is the air pressure, and Vu is the initial velocity of the aseguro projectile, said first computing circuit including a first variable circuit element representing the factor r, and means coupled to said first variable circuit element and responsive to solutions of said first equation other than zero for varying said first variable circuit element until a zerq solution is obtained; a second computing circuit for electrically solving for Vm a second equation:

where t is the time of fiight of the projectile from the aircraft to the target, said second computing circuit including a second variable circuit element representing the factor 1'; and means coupled to the first-named means for varying said second variable circuit element simultaneously with said tirst variable circuit element.

4. A ballistics computer for computing the average velocity Vm of a projectile discharged from an aircraft relative to the velocity Va of the aircraft, said computer comprising: a first computing circuit for electrically solving for Vm as a function of Va, initial velocity V of the projectile, time of flight t of the projectile from the aircraft to the target, and a variable quantity r, said first computing circuit including a variable circuit element representingT said variable quantity r; a second computing circuit for electrically solving for said variable quantity r as a function of VD, Va, air temperature T, and air pressure P; and means coupled between said first and second computing circuits for varying said variable circuit element in accordance with the solution for r obtained by said second computing circuit.

5. A ballistics computer for computing the average velocity Vm of a projectile discharged from an aircraft relative to the velocity Va of the aircraft, said computer comprising: a first computing circuit for electrically solving for a factor r a first equation CV=rp(V0+1/2 Va), where C is a predetermined constant, V0 is the initial velocity of' the projectile. and p is the air density, said first computing circuit including a first variable circuit lement representing the factor t' in said first computing circuit, and means coupled to said first variable circuit element and responsive to electrical signals in said first computing circuit representative of inequalities in the two sides of said first equation for varying said first vaiiable circuit element to eliminate said electrical signals; a second computing circuit for electrically solvinft for Vm a second equation:

TVO-tifa where t is the time of liight of the projectile from the aircraft to the target, said second computing circuit including a second variable circuit element representing the factor r in said second computing circuit; and means coupled to the first-named means for varying said second variable circuit element simultaneously with said first variable circuit element.

6. A ballistics computer for computing the average velocity Vm of a projectile discharged from an aircraft relative to the velocity Va of the aircraft, said computer comprising: a first computing circuit for electrically Solving for Vm as a function of Vn, initial velocity V0 of the projectile, time of flight t of the projectile from the aircraft to the target, and a variable quantity r, said first computing circuit including a variable circuit element representing the variable quantity r in said rst computing circuit; a second computing circuit for electrically solving for the variable quantity r as a function of V0, Va, and air density p; and means coupled between Said second computing circuit and said variable circuit element for varying said variable circuit element in accordance with the solution for r obtained by said second computing circuit.

7. A ballistics computer for computing the average velocity Vm of a projectile discharged from an aircraft relative to the velocity Va of the aircraft as a function of Va, the initial velocity V0 of the projectile, the air temperature T, the air pressure P, and time of flight t of the projectile from the aircraft to the target, said computer comprising: a first electrical circuit for combining a pair of electrical signals representing V0 and Va, respectively, to produce a first electrical output signal representing P( VO-l-l/z Va); a rst variable circuit element for producing a second electrical output signal equal to said first output signal multiplied by the factor r; a sec ond electrical circuit for receiving an electrical signal representing T and producing a third electrical output signal representing DT, where D is a predetermined constant; a third electrical circuit for combining said pair of electrical signals representing V0 and Va to produce a fourth electrical output signal representing Vm, said third electrical circuit including a second variable circuit element representing said factor r; a mixer for combining said second and third electrical output signals to produce a fth electrical output signal proportional to the difierence between said second and third electrical output signals; and means coupled to said first variable circuit element and responsive to said fifth electrical output signal for varying said first variable circuit element to reduce said fifth electrical output signal to zero, said means being coupled to said second variable circuit element for varying said second variable circuit element simultaneously with the variation of said rst variable circuit element.

8. In a ballistics computer for computing the average velocity of an aircraft, wherein said computer includes a first computing circuit having a first variable circuit element representing one variable quantity involved in the computation of the average velocity, said one variable quantity being proportional to the ratio of a first variable to a second variable, the combination comprising: a second variable circuit element for receiving an electrical signal representing said second variable and producing a rst electrical output signal representing said second variable multiplied by said one variable quantity; a mixer for combining said first electrical output Signal with an electrical signal representing said first variable to produce a second electrical output signal proportional to the difference between said first electrical output signal and said electrical signal representing said first variable; and follow-up means coupled to said second variable circuit element and responsive to said second electrical output signal for `i/arying said second variable circuit element to reduce said second electrical output signal to zero. said follow-up means being coupled to said first variable circuit element for varying said first variable circuit element simultaneously with said second variable circuit element.

9. ln an electrical computing system for computing the value of an unknown, wherein said system includes a computing circuit having a first variable circuit element representing a factor involved in the computation of the unknown, said factor being proportional to the ratio of a first variable to a second variable, the combination comprising: a second variable circuit element for receiving an electrical signal representing said second variable and producing a first electrical output signal representing said second variable multiplied by said factor; a mixer for combining said first electrical output signal with an electrical signal representing said first variable to nroduce a second electrical output signal proportional to the difference between said first electrical output signal and said electrical signal representing said first variable; means coupled to said second variable circuit element and r3- sponsive to said second electrical output signal for varying said second variable circuit element until the magnitude of said first electrical output signal is equal to that of the electrical signal representing said first variable; and means coupled to the last-named means for varying said first variable circuit element simultaneously with said second variable circuit element.

l0. An electrical computing system for computing the il value of an unknown X as a function of a plurality of variables, v, ir, x, and y, the variable v being a function of x, y and a variable z, said system comprising: a rst electrical computing circuit for computing tne value of the unknown t'x-uu/ u--'w and indicating the computed value of X as un electrical signal. said first electrical computing circuit including a variable circuit element representing v, a second electrical computing circuit for computing the value of the variable Imam-kay) i where IQ and k2 are constants und means coupled bctwccu Suid secondY electrical computing circuit and said variable circuit element for varying said variable circuit element References Cicd in the lc of this patent UNTED STATES PATENTS 2,408,081 Lovell et nl Sept. 2+', 1946 2,494,036 Darlington Inn. 10,"1950 2,545,655 Doyle Mar. 20, l95l FOREIGN PATENTS 625,023 Great Britain J'unc 21, 1949 OTHER REFERENCES Electronic Instruments by Greenwood, Holdurn and MacRae, 'l :V dio Laboratory Scrics. vol. 3l. published by 'icGraw-Hill in 1948. (Patent Olicc Technical Library; No. TK 7870 G7; reference is to page 139.)

UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 2,833,470 May 6, i958 William R. Welty It is hereby certified that error appears in the printed specification of the above numbered patent requiring correction and thatl the .said Letters Patent should read as corrected below.

Column 8, line 13, for empirical read empirically-g column 4, line 22, for that portion of the equation reading t t I read f 0 0 column 5, line 22, for l7a=0, read -l7= lines 26 and 27, for the equation -V=o=%Y read mgm VF@ Signed and sealed this 14th day of October 1958.

[SEAL] Attest: KARL I-I. AXLINE, ROBERT C. WATSON, Attestz'ng Oycer. ommz'ssz'oner of Patents. 

